Binomial Probabilities

To compute the probability of a certain number of outcomes (k) of a certain number of attempts (n), given that the probability of that outcome is p, is:

nCk * pk * (1-p)(n - k)

Where nCk means the number of combinations of n taken k at a time. This is:
n!
k! (n - k)!

Using a Javascript Function to Compute

It is easy to write a small web page that allows the user to type in certain values in a text field and make a small program in Javascript to compute a result based on these values. First define a form and some text fields to hold the values of n, k and p:
n =
k =
p =

Exact Probability =
That Successes Or More =
That Successes or Less =

Then define a script which is called when the user presses the button. To see how this works, View the page source. Save this page and see if you can write your own web page that can compute the probability of k or more outcomes. To check your work, the probability of 3 successes of 5 attempts (with p=.6) is 0.346 and the the probability of 3 or more is .683. To see javascript errors type "javascript:" in the web page location of your browser. See if you can use your web page to answer question 25 of the Chapter 4 Quiz